A note on the injective dimension of local cohomology modules
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- by M. Hellus
- Proc. Amer. Math. Soc. 136 (2008), 2313-2321
- DOI: https://doi.org/10.1090/S0002-9939-08-09198-3
- Published electronically: February 28, 2008
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Abstract:
For a Noetherian ring $R$ we call an $R$-module $M$ cofinite if there exists an ideal $I$ of $R$ such that $M$ is $I$-cofinite; we show that every cofinite module $M$ satisfies $\dim _R(M)\leq \operatorname {injdim}_R(M)$. As an application we study the question which local cohomology modules $H^i_I(R)$ satisfy $\operatorname {injdim}_R(H^i_I(R))=\dim _R(H^i_I(R))$. There are two situations where the answer is positive. On the other hand, we present two counterexamples, the failure in these two examples coming from different reasons.References
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Bibliographic Information
- M. Hellus
- Affiliation: Fakultät für Mathematik und Informatik, Universität Leipzig, PF 10 09 20, D-04009 Leipzig, Germany
- MR Author ID: 674206
- Email: hellus@math.uni-leipzig.de
- Received by editor(s): October 26, 2006
- Received by editor(s) in revised form: February 28, 2007, and April 2, 2007
- Published electronically: February 28, 2008
- Communicated by: Bernd Ulrich
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2313-2321
- MSC (2000): Primary 13D45; Secondary 13C05
- DOI: https://doi.org/10.1090/S0002-9939-08-09198-3
- MathSciNet review: 2390497